Method of aligning pixelated light engines

ABSTRACT

A three-dimensional printing system is for fabricating or manufacturing a three-dimensional article. The three-dimensional printing system includes a substrate, a light engine, a radiation sensor, and a controller. The substrate has a surface positioned proximate to a build field. The surface supports a calibration target which includes or defines elongate light modulating bars disposed at two different orientations and including a Y-bar aligned with a Y-axis and an X-bar aligned with an X-axis. The light engine includes a plurality of projection modules including at least a first projection module and a second projection module. The first projection module configured to project an array of pixels onto a first image field. The second projection module configured to project an array of pixels onto a second image field.

CROSS-REFERENCE TO RELATED APPLICATIONS

This non-provisional patent application claims priority to U.S.Provisional Application Ser. No. 62/842,565, Entitled “Method ofAligning Pixelated Light Engines” by Kirt Winter, filed on May 3, 2019,incorporated herein by reference under the benefit of U.S.C. 119(e).

FIELD OF THE INVENTION

The present disclosure concerns an apparatus and method for the digitalfabrication of three dimensional articles of manufacture through thesolidification of liquid photon-curable (photocure) resins using plurallight engines. More particularly, the present disclosure concerns anaccurate and efficient method of aligning plural light engines toprovide large, high quality articles of manufacture.

BACKGROUND

Three dimensional (3D) printers are in rapidly increasing use. One classof 3D printers includes stereolithography printers having a generalprinciple of operation including the selective curing and hardening ofradiation curable (photocurable) liquid resins. A typicalstereolithography system includes a resin vessel holding thephotocurable resin, a movement mechanism coupled to a support surface,and a controllable light engine. The stereolithography system forms athree dimensional (3D) article of manufacture by selectively curinglayers of the photocurable resin onto a “support fixture.” Eachselectively cured layer is formed at a “build plane” or “build field”within the resin.

One class of stereolithography systems utilizes light engines based onspatial light modulators such as arrays of micromirrors. Such systemsare generally limited by the pixel count of the spatial light modulator.There is a desire to provide systems having larger numbers of pixels toform larger and higher resolution articles of manufacture.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic diagram of an embodiment of a three-dimensionalprinting system for manufacturing or fabricating a three-dimensionalarticle.

FIG. 2 is a schematic diagram depicting an embodiment of a targetoverlaying a build field.

FIG. 3 is a diagram of a spatial sequence of pixel columns that areprojected onto a portion of a target.

FIG. 4 is a graph of sensed intensity versus pixel column location.

FIG. 5 is a flowchart of an embodiment of a method of aligning aprojection module to a target along one axis.

FIG. 6 is a diagram of a spatial sequence of pixel columns that areprojected onto a portion of a target. The spatial sequence of pixelcolumns have an exaggerated theta-z angular alignment error with respectto the target.

FIG. 7A is a graph of sensed intensity versus pixel array location inwhich the pixel columns have a relatively small theta-z angularalignment error with respect to the target.

FIG. 7B is a graph of sensed intensity versus pixel array location inwhich the pixel columns have a relatively large theta-z angularalignment error with respect to the target.

FIG. 8 is a flowchart depicting an embodiment of a method of angularlyaligning a projection module to a target with respect to theta-Z.

FIG. 9 is a flowchart depicting an embodiment of an overall processsequence for aligning a plurality of projection modules of athree-dimensional printing system.

SUMMARY

In a first aspect of the disclosure, a three-dimensional printing systemis for fabricating or manufacturing a three-dimensional article. Thethree-dimensional printing system includes a substrate, a light engine,a radiation sensor, and a controller. The substrate has a surfacepositioned proximate to a build field. The build field is for hardeninglayers of a build material during fabrication of the three-dimensionalarticle. The surface supports a calibration target which includes ordefines elongate light modulating bars disposed at two differentorientations and including a Y-bar aligned with a Y-axis and an X-baraligned with an X-axis. The light engine includes a plurality ofprojection modules including at least a first projection module and asecond projection module. The first projection module is configured toproject an array of pixels onto a first image field. The secondprojection module is configured to project an array of pixels onto asecond image field. The image fields of the light engine cover the buildfield including at least one overlap field between the first image fieldand the second image field. The radiation sensor receives light from thecalibration target that is reflected, emitted, or transmitted. Thecontroller is configured to: (1) operate the first projection module toproject a first sequence of columns of pixels onto the target; thecolumns are individually approximately angularly aligned with theY-axis; the first temporal sequence of columns are separated from eachother along the X-axis; (2) operate the radiation sensor to measure anintensity of light from the target during the first sequence; (3) storefirst information indicative of the measured intensity versus columnaxial position; (4) analyze the stored first information to align thefirst projection module to the calibration target along the X-axis. Theprojected columns of light are spatially and temporally separated fromeach other so that the radiation sensor receives light originating fromone projected column at a time. The target can be either a light fieldor dark field target. The system can further include a resin vessel forcontaining photocurable resin to be selectively cured by the lightengine and a support plate for alternately supporting the resin vesseland the substrate.

In one implementation the stored information defines an intensityreceived by the sensor versus position of column of pixels. Theintensity versus position includes a perturbation caused by the Y-bar.Analyzing includes finding the center of the perturbation to find thecenter of the Y-bar.

In another implementation the controller is configured to: (a) operatethe second projection module to project a second sequence of columns ofpixels onto the target; the second sequence of columns of pixels areindividually approximately angularly aligned with the Y-axis; the secondtemporal sequence of columns are separated from each other along theX-axis; (b) operate the radiation sensor to measure an intensity oflight from the target during the second sequence; (c) store secondinformation indicative of the measured intensity versus column axialposition; (d) analyze the stored second information to align the secondprojection module to the calibration target along the X-axis. The firstsequence of columns of pixels are aligned to a first Y-bar within thefirst image field and outside of the second image field. The secondsequence of pixels are aligned to a second Y-bar that is located withinthe second image field and outside of the first image field.

In yet another implementation the controller is configured to: (a)operate the second projection module to project a second sequence ofcolumns of pixels onto the target; the second sequence of columns ofpixels are individually approximately angularly aligned with the Y-axis;the second temporal sequence of columns are separated from each otheralong the X-axis; (b) operate the radiation sensor to measure anintensity of light from the target during the second sequence; (c) storesecond information indicative of the measured intensity versus columnaxial position; (d) analyze the stored second information to align thesecond projection module to the calibration target along the X-axis. Thefirst and second sequence of pixels are aligned to the same Y-bar withinan overlap field between the first image field and the second imagefield.

In a further implementation the controller is configured to: (a) operatethe first projection module to generate a third sequence of rows ofpixels onto the target, the rows are individually approximatelyangularly aligned with the X-axis; the third sequence of rows aredisplaced from each other along the Y-axis; (b) operate the radiationsensor to measure an intensity of light from the target during the thirdsequence; (c) store third information indicative of the measuredintensity versus column position; (d) analyze the stored thirdinformation to align the first projection module to the calibrationtarget along the Y-axis.

In a yet further implementation the controller is configured to: (a)operate the first projection module to generate a plurality of sequencesof columns of pixels onto the target having a varying theta-Zorientation with respect to a vertical Z-axis; each column within asequence of columns being displaced from each other along the X-axis;(b) operate the radiation sensor to measure an intensity of light fromthe target during the plurality of sequences; (c) store fourthinformation indicative of the measured intensity versus column positionfor a plurality of intensity versus position curves that each correspondto one of the sequences; (d) analyze the fourth information to angularlyalign the first projection module to the calibration target with respectto theta-Z. The analyzing can include selecting an orientationcorresponding to one or more of: (1) a maximized slope of intensityversus position for a transition at the edge of a Y-bar, (2) minimize awidth of a perturbation from a field intensity, and (3) maximize a widthof an intensity extremum corresponding to complete overlap between apixel column and a Y-bar.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a schematic diagram of a three-dimensional printing system 2.In describing the three dimensional printing system 2, mutuallyperpendicular axes X, Y and Z will be used. Axes X and Y are lateralaxes. In some embodiments X and Y are also horizontal axes. In someembodiments Z is a vertical axis. In some embodiments the direction +Zis generally upward and the direction −Z is generally downward. Inaddition, a rotational coordinate theta-Z or θ_(z), will be used.Theta-Z refers to rotation about the vertical Z-axis.

System 2 includes a support plate 4 for supporting a resin vessel 6above a light engine 8 during manufacture or fabrication of athree-dimensional article. The resin vessel 6 is for containing aphotocurable resin 10. The photocurable resin 10 is selectively cured bythe light engine 8 in a layer-by-layer manner during manufacture of thethree-dimensional article. The selective curing occurs across a lateralbuild field 20 that is at a certain height above the light engine 8.

In the illustrated embodiment a transparent substrate 12 is showninstalled upon the support plate 4. The transparent substrate 12 has anupper surface 14 that supports a target 16. The target 16 defines apattern 18 that is used for aligning portions of light engine 8. In someembodiments, the target 16 can be formed directly onto the substrate 12.In an illustrative embodiment, the target 16 is a material sheet with aprinted pattern 18. The printed pattern 18 is positioned at the buildfield 20.

The light engine 8 includes two or more projection modules 9 includingat least a first projection module 9A and a second projection module 9B.The first projection module 9A and the second projection module 9Bseparately image different portions of the build field 20 but they alsoimage an overlapping portion as will be discussed in more detail withrespect to FIG. 2.

A radiation sensor 22 is positioned either above or below the buildfield 20. Sensor 22 is configured to sense radiation that is eithertransmitted by, re-emitted by, or reflected by the target 16.

A controller 24 is coupled to the light engine 8 and the sensor 22. Thecontroller 24 includes a processor 26 coupled to an information storagedevice 28. The information storage device 28 includes a non-transitorycomputer readable storage medium that stores software instructions. Inresponse to execution by the processor, the software instructionsoperate and monitor the light engine 8, the sensor 22, and otherportions of system 2.

FIG. 2 is a diagram depicting an embodiment of the target 16 and thebuild field 20 superposed. The embodiment of FIG. 2 is a result of asystem 2 having four projection modules 9A-D. The build field 20 is acomposite of four image fields 21A, 21B, 21C, and 21D that correspond tothe projection modules 9A-D.

The image fields 21 individually include a non-overlapping zone 30 thatis imaged by a single projection module 9. For example, non-overlappingzone 30A of image field 21A is imaged by only the projection module 9A.The build field 20 also has overlap zones 32 within which two or moreimage fields 21 overlap. For example, overlap zone 32AB is a rectangularzone over which image fields 21A and 21B overlap. The overlap zone32ABCD is a rectangular zone over which all four image fields 21A-Doverlap.

In an illustrative embodiment, the target 16 includes a sheet ofmaterial that either reflects, transmits, and/or fluoresces in responseto radiation from the light engine 8. The target includes a plurality ofelongate printed light modulating lines or bars of varying widthincluding X-bars (34, 38) and Y-bars (36, 40) which are further referredto as wide X-bars 34, wide Y-bars 36, narrow X-bars 38, and narrowY-bars 40. In FIG. 2, element numbers also include letter indicia toindicate which image fields 21 are overlaid. For example, the wide X-bar34AC passes through the image fields 21A and 21C. Narrow Y-bar bar 40CDpasses through image fields 21C and 21D. Narrow X-bar bar 38ABCD passesthrough all four image fields 21A-D.

In the illustrative embodiment there can be four sensors 22A-Dcorresponding to the four image fields 21A-D. The four sensors 22A-D canbe individually positioned directly above or below an approximate centerof the corresponding image field 21A-D which is approximately where awide X-bar 34 crosses a wide Y-bar 36. For example, sensor 22A is placedabove or below the intersection of the X-bar 34AC and the Y-bar 36AB.

The controller 24 is configured to operate the projection modules 9,capture information from sensors 22, and to analyze the information toalign the image fields 21 of the projection modules 9 relative to thetarget 16 and to each other. In doing so, the wide X-bars 34 are used toindividually align the projection modules 9 to the target 16 along theY-axis. The wide Y-bars 36 are used to individually align the projectionmodules 9 to the target along the X-axis. Inner narrow X-bar 38ABCD andY-bar 40ABCD can be used to fine tune alignment of the projectors withrespect to each other. Outer narrow X-bars 38 and Y-bars 40 can be usedto compensate for distortion such as barrel distortion and keystonedistortion.

FIG. 3 is a diagram superposing a spatial sequence 42 of pixel 44columns 46 onto a portion of the target 16 which is superposed with anon-overlapping portion 30A of image field 21A. Target 16 includes aportion of wide Y-bar 36AB. The columns of pixels are generated atdifferent times so that useful sensor data can be captured.

The arrows labeled x1, x2, and so on indicate pixel columns 46 that areprojected onto the target 16 at different axial locations (generallyalong the X-axis) by the projection module 9A. At axial location x1, thecolumn above the arrow x1 is projected. At axial location x2, the columnabove the arrow x2 is projected. The axial location indicators x1, x2,x3, etc., also correspond to different times. In other words, at aparticular time, a single one of the columns are projected to avoidconfounding a signal captured by sensor 22A. The columns 46 can beprojected in any temporal order.

When a pixel column 46 is projected onto the light (white) area of thetarget, a relatively maximum intensity of radiation is received by thesensor 22A because the radiation is either reflected, re-emitted (as alonger wavelength), or transmitted to the sensor 22A. Thus, the pixelcolumn 46 displayed at X-axis locations x1, x2, x8, and x9 will tend toresult in a maximum radiation signal for the sensor 22A.

On the other hand, when a pixel column is projected fully onto the darkarea (Y-bar 36AB) of the target, a relatively minimum intensity ofradiation is received by sensor 22A. Thus, the pixel columns 46displayed at X coordinates x4, x5, and x6 will tend to result in aminimum radiation signal.

The pixel columns 46 for x3 and x7 partially overlap the Y-bar 36AB andso an intermediate intensity of radiation is received by sensor 22A.Thus, the pixel columns 46 displayed at x3 and x7 will tend to result inan intermediate radiation signal.

FIG. 4 is an approximate graph of intensity received by sensor 22Aversus position x which corresponds to FIG. 3. Some of the x-valuesincluding x1, x3, and x5 from FIG. 3 are indicated. As shown, theintensity is maximized whenever the pixel column 46 is away from a Y-bar36 as at value x1. When the pixel column 46 partially overlaps theY-bar, the intensity is at an intermediate level as at x3. When thepixel column 46 is fully within the Y-bar 36, the intensity is minimizedas at x5.

Various metrics can be computed using the data from the graph of FIG. 4.A time XE (width of extremum) is a width of the graph at which theintensity is at minimum. A width XW is a width of the overallperturbation caused by the Y-bar 36. Yet another metric would be amagnitude of a slope (m) of the graph at time x3 and/or time x7 in atransition between a high intensity and a low intensity signal. Afurther metric would be a ratio of XE to XW.

FIG. 5 is a flowchart of a method of aligning a projection module 9 tothe target 16. According to 50, a sequence of pixel arrays is generatedand projected onto the target 16. Each of the sequence of pixel arraysis displayed at a different axial location. FIG. 3 previouslyillustrated the pixel arrays as pixel columns 46 displayed at axiallocations x1, x2, and so on.

According to 52, concurrent with the sequence generation, a sensor 22receives the radiation and outputs a signal to the controller 24.According to 54, the signal is analyzed to align the projection module 9to the target 16.

In one embodiment of FIG. 4 a center of the perturbation (deflectionfrom maximum intensity) is computed to be a center of the Y-bar alongthe X-axis. This center can be aligned to a corresponding pixel column46 or an interpolation between two pixel columns 46.

FIG. 3 depicts the pixel column 46 as being very nearly parallel to theY-bar 36. However, the Y-bar may not be perfectly parallel. FIG. 6depicts a situation in which the pixel row 46 is angularly misalignedabout the Z-axis (in Theta-Z) relative to the Y-bar 36. The angular skewof FIG. 6 is exaggerated for illustrative purposes to facilitateexplanation.

FIGS. 7A and 7B show the comparison of intensity versus X sequences(like FIG. 4) that are obtained when the angular misalignment isrelatively small (FIG. 7A) and large (FIG. 7B). Therefore, FIG. 7Acorresponds to the pixel column sequence of FIG. 3 and FIG. 7Bcorresponds to the pixel column sequence of FIG. 6. As the angularalignment improves, several changes occur. First, the slope m of thegraph between minimum intensity and maximum intensity increases. At thesame time, the width XW (see FIG. 4) decreases. Third, the width XEincreases. Fourth, a ratio of XE to XW converges on unity.

FIG. 8 is a flowchart depicting a method 58 of angularly aligning aprojection module 9 to a target 16. According to 60, a sequence of pixelarrays is generated and projected onto the target 16. According to 62,concurrent with the sequence generation, a sensor 22 receives theradiation and outputs a signal to the controller 24. According to 64, adata set characterizing the signal is stored. The data set can define agraph such as that depicted in FIG. 4. Steps 60-64 are repeated forvarying orientations of the pixel arrays and the characterizing datastored.

According to 66, the data sets are analyzed to align the projectionmodule 9 to the target 16. This can be done by analyzing metrics such asthe slope m, width XE, or width XW. The angular orientation of a pixelarray for which slope m is maximized, XE is maximized, and/or XW isminimized would be the closest angular alignment to the Y-bar 36.

FIG. 9 is a flowchart depicting an overall process sequence 68 foraligning the projection modules 9 of a three-dimensional printing system2. According to 70, the individual projection modules are aligned in Xand Y to the target 16. For a single projection module, this includesperforming the method 48 twice—once aligning to the Y-bar and thenaligning to the X-bar.

According to 72, the projection modules 9 are individually aligned tothe target 16 in theta-Z. This can include performing method 58 for eachprojection module 9.

According to 74, the alignment can be performed in the overlappingregions 32 using thin X-bar 38 and thin Y-bar 40. The method of step 74is essentially the same as method 48, and serves to refine alignmentaccuracy between the projection modules 9.

According to FIG. 76, further processes can be performed using the outerthin X-bars 38 and thin Y-bars 40 to provide data to correct fordistortions such as barrel distortions and keystone errors. Generatingdata sets for such corrections can employ methods similar or related tothose discussed with respect to FIGS. 3-8.

Methods have been described with respect to FIGS. 2-9 using a lightfield target (white or clear target with dark bars). However, verysimilar methods can be performed using dark field targets in which theindicia are clear or white and the field is dark or black.

Although the above disclosure has been described in terms of aligningplural projectors, some of the apparatus and techniques above may beapplicable to correcting distortions for a system having a singleprojector. The specific embodiments and applications thereof describedabove are for illustrative purposes only and do not precludemodifications and variations encompassed by the scope of the followingclaims.

What is claimed:
 1. A three-dimensional printing system for fabricatinga three-dimensional article comprising: a substrate having a surfacepositioned proximate to a build field, the build field for hardeninglayers of a build material, the surface supporting a calibration target,the calibration target including elongate light modulating bars that aredisposed at two different orientations including a Y-bar aligned with aY-axis and an X-bar aligned with an X-axis; a light engine that includesa plurality of projection modules including at least a first projectionmodule and a second projection module, the first projection moduleconfigured to project an array of pixels onto a first image field, thesecond projection module configured to project an array of pixels onto asecond image field, the image fields of the light engine covering thebuild field and including at least one overlap field; a radiation sensorthat receives light from the calibration target; and a controllerconfigured to: operate the first projection module to project a firstsequence of columns of pixels onto the target, the columns areindividually approximately angularly aligned with the Y-axis, the firstsequence of columns are separated from each other along the X-axis;operate the radiation sensor to measure an intensity of light from thetarget during the first sequence; store first information indicative ofthe measured intensity versus column axial position; and analyze thestored first information to align the first projection module to thecalibration target along the X-axis.
 2. The three-dimensional printingsystem of claim 1 wherein the stored first information defines anintensity received by the sensor versus position of column of pixels,the intensity versus position includes a perturbation caused by theY-bar, analyzing includes finding the center of the perturbation to findthe center of the Y-bar.
 3. The three-dimensional printing system ofclaim 1 wherein the controller is configured to: operate the secondprojection module to project a second sequence of columns of pixels ontothe target, the second sequence of columns of pixels are individuallyapproximately angularly aligned with the Y-axis, the second sequence ofcolumns are separated from each other along the X-axis; operate theradiation sensor to measure an intensity of light from the target duringthe second sequence; store second information indicative of the measuredintensity versus column axial position; and analyze the stored secondinformation to align the second projection module to the calibrationtarget along the X-axis.
 4. The three-dimensional printing system ofclaim 3 wherein the first sequence of columns of pixels are aligned to afirst Y-bar within the first image field and outside of the second imagefield, the second sequence of pixels are aligned to a second Y-bar thatis located within the second image field and outside of the first imagefield.
 5. The three-dimensional printing system of claim 3 wherein thefirst and second sequence of pixels are aligned to the same Y-bar withinan overlap field between the first image field and the second imagefield.
 6. The three-dimensional printing system of claim 1 wherein thecontroller is configured to: operate the first projection module togenerate a third sequence of rows of pixels onto the target, the rowsare individually approximately angularly aligned with the X-axis, thethird sequence of rows are displaced from each other along the Y-axis;operate the radiation sensor to measure an intensity of light from thetarget during the third sequence; store third information indicative ofthe measured intensity versus column position; and analyze the storedthird information to align the first projection module to thecalibration target along the Y-axis.
 7. The three-dimensional printingsystem of claim 1 wherein the controller is configured to: operate thefirst projection module to generate a plurality of sequences of columnsof pixels onto the target having a varying theta-Z orientation withrespect to a vertical Z-axis, each column within a sequence of columnsbeing displaced from each other along the X-axis; operate the radiationsensor to measure an intensity of light from the target during theplurality of sequences; store fourth information indicative of themeasured intensity versus column position for a plurality of intensityversus position curves that each correspond to one of the sequences; andanalyze the stored fourth information to angularly align the firstprojection module to the calibration target with respect to theta-Z. 8.The three-dimensional printing system of claim 7 wherein analyzingincludes selecting an orientation corresponding to one or more of: (1) amaximized slope of intensity versus position for a transition at theedge of a Y-bar, (2) minimize a width of a perturbation from a fieldintensity, and (3) maximize a width of an intensity extremumcorresponding to complete overlap between a pixel column and a Y-bar. 9.The three-dimensional printing system of claim 1 wherein the target is alight field target and the modulating bars have an increased absorptionof the radiation relative to the light field.
 10. The three-dimensionalprinting system of claim 1 further comprising a resin vessel forcontaining photocurable resin to be selectively cured by the lightengine and a support plate for alternately supporting the resin vesseland the substrate.
 11. A method of operating a three-dimensionalprinting system for manufacturing a three-dimensional articlecomprising: positioning a substrate surface proximate to a build field,the build field for hardening layers of a build material, the surfacesupporting a calibration target, the calibration target includingelongate light modulating bars that are disposed at two differentorientations including a Y-bar aligned with a Y-axis and an X-baraligned with an X-axis; operating a light engine that includes aplurality of projection modules including at least a first projectionmodule and a second projection module, the first projection moduleconfigured to project an array of pixels onto a first image field, thesecond projection module configured to project an array of pixels onto asecond image field, the image fields of the light engine covering thebuild field and including at least one overlap field, operating thelight engine includes operating the first projection module to generatea first sequence of columns of pixels onto the target, the columns areindividually approximately angularly aligned with the Y-axis, the firstsequence of columns are displaced from each other along the X-axis;operating a radiation sensor to measure an intensity of light from thetarget during the first sequence; storing first information indicativeof the measured intensity versus a column position from the radiationsensor; and analyzing the stored first information to align the firstprojection module to the calibration target along the X-axis.
 12. Themethod of claim 11 wherein the stored first information defines anintensity received by the sensor versus position of column of pixels,the intensity versus position includes a perturbation caused by theY-bar, analyzing includes finding the center of the perturbation to findthe center of the Y-bar.
 13. The method of claim 11 further comprising:operating the second projection module to project a second sequence ofcolumns of pixels onto the target, the second sequence of columns ofpixels are individually approximately angularly aligned with the Y-axis,the second sequence of columns are separated from each other along theX-axis; operating the radiation sensor to measure an intensity of lightfrom the target during the second sequence; storing second informationindicative of the measured intensity versus column axial position; andanalyzing the stored second information to align the second projectionmodule to the calibration target along the X-axis.
 14. The method ofclaim 13 wherein the first sequence of columns of pixels are aligned toa first Y-bar within the first image field and outside of the secondimage field, the second sequence of pixels are aligned to a second Y-barthat is located within the second image field and outside of the firstimage field.
 15. The method of claim 13 the first and second sequence ofpixels are aligned to the same Y-bar within an overlap field between thefirst image field and the second image field.
 16. The method of claim 11further comprising: operating the first projection module to generate athird sequence of rows of pixels onto the target, the rows areindividually approximately angularly aligned with the X-axis, the thirdsequence of rows are displaced from each other along the Y-axis;operating the radiation sensor to measure an intensity of light from thetarget during the third sequence; storing third information indicativeof the measured intensity versus column position; and analyzing thestored third information to align the first projection module to thecalibration target along the Y-axis.
 17. The method of claim 11 furthercomprising: operating the first projection module to generate aplurality of sequences of columns of pixels onto the target having avarying theta-Z orientation with respect to a vertical Z-axis, eachcolumn within a sequence of columns being displaced from each otheralong the X-axis; operating the radiation sensor to measure an intensityof light from the target during the plurality of sequences; storingfourth information indicative of the measured intensity versus columnposition for a plurality of intensity versus position curves that eachcorrespond to one of the sequences; and analyzing the stored fourthinformation to angularly align the first projection module to thecalibration target with respect to theta-Z.
 18. The method of claim 17wherein analyzing includes selecting an orientation corresponding to oneor more of: (1) a maximized slope of intensity versus position for atransition at the edge of a Y-bar, (2) minimize a width of aperturbation from a field intensity, and (3) maximize a width of anintensity extremum corresponding to complete overlap between a pixelcolumn and a Y-bar.
 19. The method of claim 11 further comprising:performing additional calibration operations with the substrate surfacepositioned; removing the substrate from the three-dimensional printingsystem; positioning a resin vessel into the three-dimensional printingsystem; and operating the three-dimensional printing system tomanufacture the three-dimensional article.